Rein isn't a reincarnation of Reinforce. She's a 'regular' unison device created from Hayate's linker core. She hasn't inherited anything from Reinforce beyond one message Reinforce implanted in Hayate's core as a note to her successor.

Reinforce, on the other hand, wasn't just a unison device, she was a lost logia. A lost logia capable of destroying planets. You can't compare Rein or Agito with her.

Example in case: Unisoning with Agito did nothing to improve Zest's health.

Gonna search official confirmation of that, still sounds like a fun idea for an Agito/Rein centric adventure fanfic xD.

On the "Lost Logia" and "Zest" thing i can't deny that those two are pretty solid arguments. That's why i mentioned that it will be Hayate the one replicating the "healing" process on a much weaker version using her book to empower Agito somehow and unlike Hayate the condition of the "recovery" will be rapidly deteriorating allowing Signum/Agito only a small amount of time to fight on decent conditions. Of course, the scenario for such a risk and untrusty method can only be logically used fi the situation demands Signum's precense, otherwise it will be pretty dumb to risk Signum and Agito's lives when there are still healthy fighters out there capable of taking action.